We will examine a construction given by Oxtoby, originally used as an example of a minimal, not uniquely ergodic dynamical system; see [1]} or [2]}.
We will construct a subshift of \(\lbrace 0, 1\rbrace ^\omega \) . The construction uses a sequence \((s_j)_{j \ge 1}\)  of natural numbers such that
\( \sum _{j=1}^{\infty } \frac{1}{s_j} < 1.\) 
